Uniform Roe coronas

Alessandro Vignatti (Paris Diderot 7)

Thursday 8th November, 2018 16:00-17:00 Maths 311B


Given a metric space (X,d), one defines a subalgebra of the space of operators on ell_2(X) called the uniform Roe algebra of (X,d). The study of these algebras comes with their intrinsic relation with coarse geometry and the coarse Baum-Connes conjecture. Our aim is to study uniform Roe coronas: quotients of uniform Roe algebras by their ideal of compact operators. With a little help from set theory, we will relate isomorphisms of uniform Roe coronas with coarse equivalence, and bijective coarse equivalence, of the underlying metric spaces. No logic knowledge will be needed, as all set theoretic considerations will be blackboxed. This is joint work with Bruno Braga and Ilijas Farah.

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